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Maths 4 Mark Question

Tabular Representation of Statistical Data · Maharashtra Board STD 9 (MSBSHSE - English Medium). 26 questions.

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Question 14 Marks
The monthly wages of 30 workers in a factory are given below:
83.0, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.
Represent the data in the form of a frequency distribution with class size 10.
Answer
Here, the maximum and minimum values of the variate are 898 and 804 respectively. So the range = 898 - 804 = 94 Here, we will take class size 10. So we must have $\frac{94}{10}$ i.e. 10 classes each of size 10. Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is: Lower limit of first class interval is;$\text{a}-\frac{\text{h}}{2}=804-\frac{10}{2}=799$
And upper limit of first class interval is:$\text{a}+\frac{\text{h}}{2}=804+\frac{10}{2}=809$
Other class limits are:
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Question 24 Marks
Write the class size and class limits in the following:
12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5.
Answer
12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5.
Class size = 17.5 - 12.5 = 5
Class Mark
Lower Class Limit
Upper Class Limit
Class Limit
12.5
12.5 - 2.5 = 10
12.5 + 2.5 = 15
15-Oct
17.5
17.5 - 2.5 = 15
17.5 + 2.5 = 20
15-20
22.5
22.5 - 2.5 = 20
22.5 + 2.5 = 25
20-25
27.5
27.5 - 2.5 = 25
27.5 + 2.5 = 30
25-30
32.5
32.5 - 2.5 = 30
32.5 + 2.5 = 35
30-35
37.5
37.5 - 2.5 = 35
37.5 + 2.5 = 40
35-40
42.5
42.5 - 2.5 = 40
42.5 + 2.5 = 45
40-45
47.5
47.5 - 2.5 = 45
47.5 + 2.5 = 50
45-50
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Question 34 Marks
The number of runs scored by a cricket player in 25 innings is as follows:
26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 15, 34, 15, 34, 6, 71, 0, 64, 15, 34, 15, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64, 47
  1. Rearrange these runs in ascending order.
  2. Determine the player, is highest score.
  3. How many times did the player not score a run?
  4. How many centuries did he score?
  5. How many times did he score more than 50 runs?
Answer
The numbers of runs scored by a player in 25 innings are:
26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 15, 34, 15, 34, 6, 71, 0, 64, 15, 34, 15, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64, 47.
  1. Runs in an ascending order are:
0, 0, 0, 0, 6, 15, 15, 15, 15, 26, 34, 34, 34, 34, 35, 39, 42, 42, 47, 48, 48, 53, 54, 64, 64, 64, 67, 71, 71, 82, 90, 124, 139.
  1. The highest number = 139
  2. The player did not score any runs 3 times.
  3. He scored 3 centuries.
  4. He scored more than 50 runs 12 times.
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Question 44 Marks
Given below is a cumulative frequency distribution table showing ages of the people living in a locality:
Age in years
No. of years
Above 108
0
Above 96
1
Above 84
3
Above 72
5
Above 60
20
Above 48
158
Above 36
427
Above 24
809
Above 12
1026
Above 0
1124
Prepare a frequency distribution table.
Answer
Age (in years)
No. of persons
Class interval
Frequency
Above 0
1124
0-12
1124 - 1026 = 98
Above 12
1026
12-24
217
Above 24
809
24-36
382
Above 36
427
36-48
269
Above 38
158
48-60
138
Above 60
20
60-72
15
Above 72
5
72-84
5 - 3 = 2
Above 84
3
84-96
3 - 1 = 2
Above 96
3
96-108
1 - 0 = 1
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Question 54 Marks
The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60
  1. Arrange these marks in ascending order 30 to 39 one group 40 to 49 second group etc.
Now answer the following:
  1. What is the lowest score?
  2. What is the highest score?
  3. What is the range?
  4. If 40 is the pass mark how many failed?
  5. How many have scored 75 or more?
  6. Which observations between 50 and 60 have not actually appeared?
  7. How many have scored less than 50?
Answer
The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100, 67, 0, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56, 44, 58, 52, 64, 98, 59, 70, 39, 50, 60.
  1.  
Group
Class
Observations
I
30-39
37, 39
II
40-49
44, 48, 48
III
50-59
50, 52, 53, 55, 56, 58, 58, 59
IV
60-69
60, 60, 60, 61, 62, 64, 67, 68
V
70-79
70, 55, 77, 78
VI
80-89
84, 88
VII
90-99
90, 98
VIII
100-109
100
  1. Highest score = 100
  2. Lowest score = 37
  3. Range = 100 - 37 = 63
  4. If 40 is the passing marks 2 students have failed.
  5. 8 students have scored 75 or more.
  6. Observation 51, 54, 57 between 50 and 60 has not actually appeared.
  7. 5 students have scored less than 50
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Question 64 Marks
The number of books in different shelves of a library is as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20
19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34
38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25
28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23
43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21
Prepare a cumulative frequency distribution table using 45 - 49 as the last class-interval.
Answer
The minimum number of bookshelves is 16
and maximum number of bookshelves is 45
Range = Maximum book shelves-Minimum book shelves = 45 - 16 = 29
Given, class interval is 45 - 49.
So, class size = 49 - 45 = 4
Therefore number of classes $=\frac{\text{Range}}{\text{Class size}}= \frac{29}{4} = 7.25$
Number of classes = 8
The cumulative frequency distribution is as follows:
No of Books
No. of Shelves (Frequency)
Cumulative Frequency
13-17
1
1
17-21
6
7
21-25
11
18
25-29
15
33
29-33
12
45
33-37
5
50
37-41
6
56
41-45
3
59
45-49
1
60
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Question 74 Marks
The daily minimum temperatures in degrees Celsius recorded in a certain arctic region are as follows:

-12.5, -10.8, -18.6, -8.4, -10.8, -4.2, -4.8, -6.7, -13.2, -11.8, -2.3, 1.2, 2.6, 0, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -2.4, 0, 3.2, 2.7, 3.4, 0, -2.4, -5.8, -8.9, -14.6, -12.3, -11.5, -7.8, -2.9.

Represent them as frequency distribution table taking -19.9 to -15 as the first class interval.
Answer
Since the first class is -19.9 to -15 Therefore, the frequency distribution in which the lower limit is included and upper limit excluded is:
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Question 84 Marks
Thirty children were asked about the number of hours they watched TV programes in the previous week. The results were found as follows:
1, 6, 2, 3, 5, 12, 5, 8, 4, 8, 10, 3, 4, 12, 2, 8, 15, 1, 17, 6, 3, 2, 8, 5, 9, 6, 8, 7, 14, 2
  1. Make a frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.
  2. How many children watched television for 15 or more hours a week.
Answer
  1. Class intervals will be 0-5, 5-10, 10-15…
The grouped frequency distribution table is as follows:
Hours
Number of children
0-5
10
5-10
13
10-15
5
15-20
2
Total
30
  1. The number of children who watched TV for 15 or more hours a week is 2 (i.e number of children in class interval 15-20).
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Question 94 Marks
The weights of new born babies are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 2.5, 3.0, 2.8, 2.8, 2.9, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4.
  1. Rearrange the weights in descending order.
  2. What is the highest weight?
  3. What is the lowest weight?
  4. Determine the range?
  5. How many babies were born on that day?
  6. How many babies weigh below 2.5Kg?
  7. How many babies weigh more than 2.8Kg?
  8. How many babies weigh 2.8Kg?
Answer
The weights of new born babies (in kg) are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 2.5, 3.0, 2.8, 2.8, 2.9, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4.
  1. The weights in descending order
3.1, 3.0, 2.9, 2.9, 2.8, 2.8, 2.7, 2.7, 2.6, 2.5, 2.5, 2.4, 2.3, 2.2, 2.1.
  1. The highest weight = 3.1Kg
  2. The lowest weight = 2.1Kg
  3. Range = 3.1 - 2.1 = 1.0Kg
  4. 15 babies were born on that particular day.
  5. 4 babies weight below 2.5Kg.
  6. Weight more than 2.8Kg are 4 babies.
  7. Weight 2 babies.
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Question 104 Marks
Heights (in cm) of 30 students of class IX are given below:
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.
Prepare a frequency distribution table with 160-164 as one of the class intervals.
Answer
Height (in cm)
Tally marks
Frequency
800-810
|||
3
810-820
||
2
820-830
||
1
830-840
|||| |||
8
840-850
||||
5
850-860
|
1
860-870
|||
3
870-880
|
1
880-890
|
1
890-900
||||
5
 
 
Total = 30
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Question 114 Marks
Write the class size and class limits in the following:
104, 114, 124, 134, 144, 154 and 164.
Answer
104, 114, 124, 134, 144, 154 and 164.
Class size = 114 - 104 = 10
Class Mark
Lower Class Limit
Upper Class Limit
Class Limit
104
99
109
99-109
114
109
119
109-119
124
119
129
119-129
134
129
139
129-139
144
139
149
139-149
154
149
159
149-159
164
159
169
159-169
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Question 124 Marks
The water bills (in rupees) of 32 houses in a certain street for the period 1.198 to 31.398 are given below:
56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 69.
Tabulate the data and present the data as a cumulative frequency table using 70 - 79 as one of the class intervals.
Answer
The minimum bill is Rs. 24
The maximum bill is Rs. 95
Range = Maximum bill - Minimum bill = 95 - 24 = 71
Given, class interval is 70 - 79.
So, Class size = 79 - 70 = 9
Therefore number of classes $=\frac{\text{Range}}{\text{Class size}} = \frac{71}{9} = 7.80$
Number of classes = 8
The cumulative frequency distribution is as follows:
Bills
No. of Houses (Frequency)
Cumulative Frequency
16-25
1
1
25-34
3
4
34-43
5
9
43-52
4
13
52-61
7
20
61-70
6
26
70-79
3
29
79-88
2
31
88-97
1
32
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Question 134 Marks
Marks scored by 40 students of class IX in mathematics are given below:
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.
Prepare a frequency distribution with class size of 10 marks.
Answer
Marks
Tally Marks
Frequency
20-30
|
1
30-40
|||
3
40-50
||||
5
50-60
|||| |||
8
60-70
|||| |||
8
70-80
|||| ||||
9
80-90
||||
4
 
 
Total = 40
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Question 144 Marks
Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution.
Answer
Number of Children
Tally Marks
Number of Families
0
||||
5
1
|||| ||
7
2
|||| |||| ||
12
3
||||
5
4
|||| |
6
5
|||
3
6
|||
3
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Question 154 Marks
Following are the ages of 360 patients getting medical treatment in a hospital on a day.
Age (in years)
10-20
20-30
30-40
40-50
50-60
60-70
No of Patients
90
50
60
80
50
30
Construct a cumulative frequency table.
Answer
Age (in years)
No. of students
Marks
Cumulative Frequency
10-20
90
Less than 20
90
20-30
50
Less than 30
140
30-40
60
Less than 40
200
40-50
80
Less than 50
280
50-60
50
Less than 60
330
60-70
30
Less than 70
360
 
N = 360
 
 
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Question 164 Marks
Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as 210-230 (230 not included).
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 218, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
Answer
Monthly Wages (in rupees)
Tally marks
Frequency
210-230
||||
4
230-250
||||
4
250-270
||||
5
270-290
|||
3
290-310
|||| ||
7
310.0-330.0
||||
5
 
 
Total = 28
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Question 174 Marks
The class size of distribution is 25 and the first class-interval is 200-224. There are seven class-intervals.
Write the class-intervals.
Answer
Given
Class size = 25
First class interval = 200-224
Seven class interval are:
200-240, 225-249, 250-274, 275-299, 300-324, 325-349, 350-374.
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Question 184 Marks
The marks scored by 55 students in a test are given below:
Marks
0-5
5-10
10-15
15-20
20-25
25-30
30-35
No. of students
2
6
13
17
11
4
2
Prepare a cumulative frequency table.
Answer
Marks
No. of Students
Marks
Cumulative Frequency
0-5
2
Less than 5
2
5-10
6
Less than 10
8
10-15
13
Less than 15
21
15-20
17
Less than 20
38
20-25
11
Less than 25
49
25-30
4
Less than 30
53
30-35
2
Less than 35
55
 
N = 55
 
 
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Question 194 Marks
Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.
Weight (in kg)
No. of students
Below 30
0
Below 30
24
Below 35
78
Below 40
183
Below 45
294
Below 50
408
Below 55
543
Below 60
621
Below 65
674
Below 70
685
Answer
Weight (in kg)
No. of students
Class interval
frequency
Below 30
24
25-30
24 - 0 = 24
Below 35
78
30-35
78 - 24 = 54
Below 40
183
35-40
183 - 78 = 105
Below 45
294
40-45
294 - 183 = 111
Below 50
408
45-50
408 - 294 = 114
Below 55
543
50-55
543 - 408 = 135
Below 60
621
55-60
621 - 543 = 78
Below 65
674
60-65
671 - 621 = 53
Below 70
685
65-70
685 - 671 = 11
 
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Question 204 Marks
The daily maximum temperatures (in degree Celsius) recorded in a certain city during the month of November are as follows:
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5, 20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1.
Represent the data in the form of a frequency distribution table with class size 11°C.
Answer
Maximum Temperature(in degree Celsius)
Tally Marks
Frequency
20.0-21.0
|||| |
6
21.0-22.0
||||
5
22.0-23.0
|||| ||||
9
23.0-24.0
||||
5
24.0-25.0
|||
3
25.0-26.0
||
2
 
 
Total = 30
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Question 214 Marks
The class size of distribution is 25 and the first class-interval is 200-224. There are seven class-intervals.
Write the class-marks of each interval.
Answer
GivenClass size = 25
Class mark = 200-224
$=\frac{200+224}{2}$
$=\frac{424}{2}$
$= 212$
Class mark = 225-249
$=\frac{225+249}{2}$
$=\frac{479}{2}$
$= 237$
Class mark = 250-274
$=\frac{250+274}{2}$
$=\frac{524}{2}$
$= 287$
Class mark = 300-324
$=\frac{300+324}{2}$
$=\frac{624}{2}$
$= 312$
Class mark = 325-349
$=\frac{325+349}{2}$
$=\frac{674}{2}$
$= 337$
Class mark = 350-374
$=\frac{350+374}{2}$
$=\frac{724}{2}$
$= 362$
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Question 224 Marks
The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the most rarest blood group among these students.
Answer
Here 9 students have blood group A, 6 as B, 3 as AB and 12 as O
So the table representing the data is as follows:
Blood Group
Number of Students
A
9
B
6
AB
3
O
12
Total
30
As 12 students have their blood group O and 3 students have their blood group as AB. Therefore the most common blood group is O and the rarest blood group is AB.
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Question 234 Marks
Why do we group data?
Answer
The data obtained in original form are called raw data. Raw data does not give any useful information and is rather confusing to mind. Data is grouped so that it becomes understandable and can be interpreted. According to various characteristics groups are formed by us. After grouping the data, we are in position to make calculations of certain values which will help us in describing and analyzing the data.
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Question 244 Marks
Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 3, 0, 1, 1, 2, 3, 2, 2, 0
Prepare a frequency distribution table for the data given above.
Answer
By observing the data given above, the following frequency table can be constructed:
Number of Heads
Frequency
0
6
1
10
2
9
3
5
Total
30
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Question 254 Marks
The following cumulative frequency distribution table shows the daily electricity consumption (in KW) of 40 factories in an industrial state.
Consumption (in KW)
No. of factories
Below 240
1
Below 270
4
Below 300
8
Below 330
24
Below 360
33
Below 390
38
Below 420
40
  1. Represent this as a frequency distribution table.
  2. Prepare a cumulative frequency table.
Answer
  1.  
Consumption(in KW)
No. of factories
Class interval
Frequency
Below 240
1
0-240
1
Below 270
4
240-270
4 - 1 = 3
Below 300
8
270-300
8 - 4 = 4
Below 330
24
300-330
24 - 8 = 16
Below 360
33
330-360
33 - 24 = 9
Below 390
38
360-390
38 - 33 = 5
Below 420
40
390-420
40 - 38 = 2
  1.  
Class interval
Frequency
Consumption(in KW)
No. of factories
0-240
1
More than 0
40
240-270
3
More than 240
40 - 1 = 39
270-300
4
More than 270
39 - 3 = 36
300-330
16
More than 300
36 - 4 = 32
330-360
9
More than 330
32 - 16 = 16
360-390
5
More than 360
16 - 9 = 7
390-420
2
More than 390
7 - 5 = 2
 
 
More than 420
2 - 2 = 0
 
N = 40
 
 
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Question 264 Marks
Write the class size and class limits in the following:
47, 52, 57, 62, 67, 72, 78, 82, 87, 92, 97, 102.
Answer
47, 52, 57, 62, 67, 72, 78, 82, 87, 92, 97, 102.
Class size = 52 - 47 = 5
Class mark
Lower class limit
Upper class limit
Class limit
47
44.5
49.5
44.5-49.5
52
49.5
54.5
49.5-54.5
57
54.5
59.5
54.5-59.5
62
59.5
64.5
59.5-64.5
67
64.5
69.5
64.5-69.5
72
69.5
74.5
69.5-74.5
77
74.5
79.5
74.5-79.5
82
79.5
84.5
79.5-84.5
87
84.5
89.5
84.5-89.5
92
89.5
94.5
89.5-94.5
97
94.5
99.5
94.5-99.5
102
99.5
104.5
99.5-104.5
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